1. 3.3 More about Contingency Tables Does the explanatory variable really seem to impact the response variable? Is it a strong or weak impact?

2. How to set up the Contingency Table Which is the explanatory variable? Which is the response variable? Be sure to put the explanatory variable in the left column, and the response variable across the top row. Complete the table with raw data. Compute the percentages by dividing by the TOTAL OF EACH ROW Check the pattern created by the HIGHEST PERCENTS in EACH ROW

3. An Overall TREND: What if the TWO LARGEST percentages are in the same column? Suppose our data looked like this… YESNOTOTAL MALE23 23/32=72%9 9/32=28%32 FEMALE120 120/147=82%27 27/147=18%147

4. Gender will not help us predict the answer to this question. There is NOT an association with gender. However, we can see that OVERALL, most people answered YES to this survey question. This is a trend. We could describe the strength of this trend as STRONG, since the percents are significantly greater than 50% Our conclusion about that trend:

5. Is there a trend or an association? YESNOTOTAL MALE23 23/32=72%9 9/32=28%32 FEMALE27 27/147=18%120 120/147=82%147

6. Examine the table… where are the TWO LARGEST percentages? YESNOTOTAL MALE23 23/32=72%9 9/32=28%32 FEMALE27 27/147=18%120 120/147=82%147 Because the higher percentages are in a DIAGONAL, we can say that there is an association between GENDER and the YES/NO answer to the survey. Knowing gender helps us to predict a person’s answer. Males are more likely to say YES and Females are more likely to say NO, based on our data.

7. A Weak Association If the two largest percentages are closer to 50%, we say that the trend or association is WEAK When the two largest percentages are closer to 100%, we say that the trend or association is STRONG But what if they are exactly 50%???????

8. No Conclusion is Supported When the two largest percentages are 50%, (or even extremely close to 50%), we say that the data does not support any conclusion. There is no clear trend or association indicated when this happens. YESNOTOTAL MALE23 23/46=50% 46 FEMALE27 27/54=50% 54

9. Examples with completed table BluePink MALE72% FEMALE35% BluePink MALE68% FEMALE32% BluePink MALE48% FEMALE51% Describe the overall results from each table of contingencies. Is there a trend? An association? No conclusion? Is your conclusion weak or strong?

10. Reminder! Do NOT make any conclusion from a table with RAW DATA. You must compute the conditional proportions (percents) before making judgements and conclusions.